On certain infinitesimal isometries of surfaces
Alois Švec (1988)
Czechoslovak Mathematical Journal
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On certain infinitesimal isometries of surfaces
On equiaffine Weingarten surfaces
Alois Švec (1987)
Czechoslovak Mathematical Journal
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On the Pick invariant
Alois Švec (1988)
Czechoslovak Mathematical Journal
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Invariants and Bonnet-type theorem for surfaces in ℝ4
Georgi Ganchev, Velichka Milousheva (2010)
Open Mathematics
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In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes...
Complete classification of surfaces with a canonical principal direction in the Euclidean space 3
Marian Munteanu, Ana Nistor (2011)
Open Mathematics
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In the present paper we classify all surfaces in 3 with a canonical principal direction. Examples of this type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space 3 is the catenoid.